William James's view of emotion is famous. Its most famous feature is his claim that emotional experience is entirely bodily:
If we fancy some strong emotion, and then try to abstract from our consciousness of it all the feelings of its characteristic bodily symptoms, we find we have nothing left behind... and that a cold and neutral state of intellectual perception is all that remains.... What kind of an emotion of fear would be left, if the feelings neither of quickened heart-beats nor of shallow breathing, neither of trembling lips nor of weakened limbs, neither of goose-flesh nor of visceral stirrings, were present, it is quite impossible to think. Can one fancy the state of rage and picture no ebullition of it in the chest, no flushing of the face, no dilatation of the nostrils, no clenching of the teeth, no impulse to vigorous action, but in their stead limp muscles, calm breathing, and a placid face? The present writer, for one, certainly cannot. The rage is as completely evaporated as the sensation of its so-called manifestations, and the only thing that can possibly be supposed to take its place is some cold-blooded and dispassionate judicial sentence, confined entirely to the intellectual realm, to the effect that a certain person or persons merit chastisement for their sins (1890/1950, vol. 2, p. 451-2).Two other features are less commonly noted. One is that emotional experience is ever-present in rich detail:
Every one of the bodily changes, whosoever it be, is felt, acutely or obscurely, the moment it occurs. If the reader has never paid attention to this matter, he will be both interested and astonished to learn how many different local bodily feelings he can detect in himself as characteristic of his various emotional moods.... Our whole cubic capacity is sensibly alive; and each morsel of it contributes its pulsations of feeling, dim or sharp, pleasant, painful, or dubious, to that sense of personality that every one of us unfailingly carries with him (p. 451).Another is that emotional experience is highly variable:
We should, moreover, find that our descriptions had no absolute truth; that they only applied to the average man; that every one of us, almost, has some personal idiosyncrasy of expression, laughing or sobbing differently from his neighbor, or reddening or growing pale where others do not.... The internal shadings of emotional feeling, moreover, merge endlessly into each other. Language has discriminated some of them, as hatred, antipathy, animosity, dislike, aversion, malice, spite, vengefulness, abhorrence, etc., etc.; but in the dictionaries of synonyms we find these feelings distinguished more by their severally appropriate objective stimuli than by their conscious or subjective tone (p. 447-448).Disagreement continues, about all three issues.
Some scholars, such as Walter Cannon and Peter Goldie have argued that bodily sensations cannot possibly exhaust emotional experience; but others, such as Antonio Damasio and Jesse Prinz, have defended accounts of emotion that are broadly Jamesian in this respect.
Some scholars, such as John Searle (p. 140) have argued that we have ever-present emotional mood experiences even if they are often fairly neutral, while others, such as Russell Hurlburt and Chris Heavey, have argued that such feeling experiences are only present about 25% of the time on average. (This issue is a dimension of the larger question of how sparse or abundant human conscious experience is in general -- a question I have argued is methodologically fraught.)
I have seen less explicit discussion of how much variability there is in emotional experience between people, but some theories seem to imply that similar emotions will tend to have similar experiential cores: Keith Oatley and P.N. Johnson-Laird, for example, seem to think that each type of emotion -- e.g., anxiety, anger, disgust -- has a "distinctive phenomenological tone" (p. 34); and Goldie, while in some places emphasizing the complex variability of emotion, in other places (as in the article linked above), seems to imply that there's a distinctive qualitative character that an emotion like fear has which one cannot know unless one has experienced that emotion type. Hurlburt, in contrast, holds that people's emotional experiences are highly variable with no common core among them (e.g., here, p. 187, Box 8.8).
For all the work on emotion that has been done in the past 120 years, we are still pretty far, I think, from reaching a well-justified consensus opinion on these questions. Such is the enduring infancy of consciousness studies.